Well, I suppose it was possible. Say, at Manzikert, the western mercenaries accidentally run into Alp Arslan scouting the battlefield and capture him (or he gets an arrow in the eye, or...), and as a result the Seljuks are thrown back (for at least a while). Arslan, or his successor, then invades Mesopotamia and the Levant first instead of attacking Byzantium. Still, the threat keeps the Byzantines somewhat allied to eachother instead of going off to kill themselves. Malik Shah's death still leads to confusion, and a Byzantine expedition manages to seize much of the Levant and Syria. The expedition contains many catholics too (seeking glory and bounty now that Sicily has mostly fallen) but the Byzantines are strong enough to keep official power, and in 1099 (although extremely bloody in the taking, as the mercenaries go wild) Jerusalem is added once more to the lands of eastern Rome.
Byzantium was at its lowest point in the years before Manzikert actually. The emperors were idiots who did not manage to rule much, the army was neglected and Byzantine prestige was going down the drain. Where would they find the leadership that would enable them to field an army and go on the offensive?
I don't see them lasting long, to be honest. They did well when under pressure, but after the demise of the Macedonian dynasty their entire political system was just anarchy, anarchy, anarchy. They driving at full speed towards the abyss.
The Seljuks weren't a threat actually, Alp Arslan was at no point interested in conquering Byzantine lands. At that time, he wanted to march on Egypt to overthrew the Shiite Caliphate. Manzikert itself also was not a cathastrophic defeat - the larger part of the Byzantine army did not even take part in the battle, and the part that did was not mauled worse than in many battles before. What turned it into a total cathastrophe was that (1) the defectors (i.e. the part of the army that did not fight) marched straight on Constantinople, (2) the emperor himself was captured and humiliated worse than any emperor had been in centuries, and (3) the Byzantines BROKE the armistice that Alp Arslan had agreed to, which led to the Turkish invasion and the establishment of the Rum sultanate.
Essentially a giant dam of shit, that had steadily filled up over decades, broke, and the shit flushed all over the Byzantine empire: Decay of army and society, decay of imperial authority within and outside the empire, disastrous decision-making on the part of the emperors and their envious rivals, and crass egoism of the aristocratic upper classes.
A victory at Manzikert would have shored up the emperor's prestige, but it would likely not have averted any of the ills that were plaguing the empire at the time. Within a couple of years, the Sicilian Normans would be staring greedily across the Adriatic, and they'd be right in the next great danger.